Although this book does not specialize in types of noise, fading models, or the details of signal detection, we will review some important cases that are relevant to tactical radio SiS. We will start with the simplest case: detecting a binary antipodal signal with equal energy, as shown in Figure 2.7, in the presence of AWGN. The AWGN causes the received signal to be in a different location of the single-dimensional Cartesian space as shown in Figure 2.7. Intuitively, one can decide that the received signal corresponds to *S*_{0} if it is positive (*S*_{i} > 0) and corresponds to *S*_{1} if it is negative (*S*_{i} < 0). Practically, a binary correlation receiver is implemented (with foreknowledge of the existing of AWGN). Here, we will focus essentially on the detection technique without diving into the mathematical representations. The AWGN creates a Gaussian distribution of the noise random variable as shown in Figure 2.11. Think of this as the projection or superimposing of the AWGN represented by the bell curve (the probability distribution function or pdf of the noise random variable) onto the signal which has energy difference (*S*_{0}(*t*) − *S*_{1}(*t*)) of *E*_{d}. The curve on the right-hand side represents the conditional pdf of the received signal *y*, given that the transmitted signal is *S*_{0}, while the curve on the left-hand side represents the conditional pdf of the received signal *y*, given that the transmitted signal is *S*_{1}. The mean of *y* is μ_{0}, given that the transmitted signal is

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